few_shots: Example:
Problem/activity:
Problem 1
The table below contains single equations in a single variable, single equations in two variables, and pairs of simultaneous equations in two variables. Check the appropriate box to show whether there is no solution, exactly 1 solution, or if there is an infinite number of solutions.
|                                                          | **           No solution          ** | **           Exactly 1 solution          ** | **           Infinite number of solutions          ** |
|----------------------------------------------------------|--------------------------------------|---------------------------------------------|-------------------------------------------------------|
|                       $${9=4x+7}$$                       |                                      |                                             |                                                       |
|                       $${y=3y+5}$$                       |                                      |                                             |                                                       |
|                    $${y={x\over2}}$$                     |                                      |                                             |                                                       |
|                     $${3x+6y-9=0}$$                      |                                      |                                             |                                                       |
|    $${x=y}$$                        $${1.25x=1.25y}$$    |                                      |                                             |                                                       |
| $${9.9=6x+8y}$$                        $${9x=2.5y-8.8}$$ |                                      |                                             |                                                       |
| $${11x-2y=1.5}$$                        $${11x-2y=2.5}$$ |                                      |                                             |                                                       |
Problem 2
Kim has a small container and a large container as shown.
[IMG]
It takes 16 of the small containers to fill the large container. Three small containers leave 1.95 gallons of space in the big container.
What is the size of each of the two containers?


Standard options: 
A. Solve linear equations in one variable.
B. Analyze and solve pairs of simultaneous linear equations.


Thought: The last three rows of the table in the first problem involves solving pairs of simultaneous linear equations. The second word problem can also be represented as two simultaneous linear equations.
Answer: B

Now, assign the following problem or activity to one or more relevant standards it aligns with.
shot_info: fl_problem_001392

8
options: Fluently multiply multi-digit whole numbers using the standard algorithm.

Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used.

Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.
problem_activity: Problem 1
a.   Here are two ways to find the area of a rectangle that is 23 units by 31 units.
[IMG]
What do the area models have in common? How are they alike?
How are they different?
If you were to find the area of a rectangle that is 37 units by 49 units, which of the two ways of decomposing the rectangle would you use? Why?
b.   You might be familiar with different ways to write multiplication calculations. Here are two ways to calculate
$$23\times31$$
.
[IMG]
In Calculation A, how are each of the partial products obtained? For instance, where does the 3 come from?
In Calculation B, how are the 23 and 690 obtained?
Look at the area models in Part (a). Which area model corresponds to Calculation A? Which one corresponds to Calculation B?
How are the partial products in Calculation A and the 23 and 690 in Calculation B related to the numbers in the area models?
Problem 2
a.   Label the area model to represent
$$37\times49$$
and to find that product.
[IMG]
Decompose each number into its base-ten units (tens, ones, etc.) and write them in the boxes on each side of the rectangle.
Label regions A, B, C, and D with their areas. Show your reasoning.
Find the product that the area model represents. Show your reasoning.
b.   Here are two ways to calculate 37 × 49. Each number with a box gives the area of one or more regions in the area model.
[IMG]
In the boxes next to each number, write the letter(s) of the corresponding region(s).
In Calculation B, which two numbers are being multiplied to obtain 333? Which two are being multiplied to obtain 1,480?
Problem 3
Estimate the following products. Then solve using the standard algorithm. If you get stuck, use an area model and/or the partial products algorithm to help.
a.
$$73\times84$$
b.
$$48\times67$$


correct_option_index: 0